What is the right term, properties panel or shelf?
Blender's naming scheme is quite confusing, especially since many creators (including me) of tutorials and howto videos don't use them consistently (and there's a reason for this mess).  So let's break it down a little.

The Blender Manual introduction says that Blender's UI can be broken up into the Main Window, which contains one or more Areas with each Area containing an Editor. Editors usually have a Header and one or more Regions. Regions then contain Panels. 

According to the Manual the highlighted area in your screenshot is called "Properties Region". It shows all properties of your currently selected object(s) and lets you also edit some additional properties for your scene. Some of them could also be changed within the Properties Editor (I'm trying to stay with the terminology here...)



This seems a little absurd but it immediately makes sense if you switch the 3D View to fullscreen area (Alt+F10). 

The reason why Blender's naming scheme is still confusing is that even Blender itself calls it Panel.